We are given a geometric progression (GP) where the first term is 3 and the 5th term is 48. We need to find the common ratio of the GP.

1. Problem Description

We are given a geometric progression (GP) where the first term is 3 and the 5th term is

4

8. We need to find the common ratio of the GP.

2. Solution Steps

Let $a$ be the first term of the geometric progression and $r$ be the common ratio. The $n$th term of a GP is given by:

$a_n = a * r^(n-1)$

We are given that the first term $a = 3$ and the 5th term $a_5 = 48$. Thus, we can write the equation for the 5th term as:

$a_5 = a * r^(5-1)$

$48 = 3 * r^4$

Now we solve for $r$:

$r^4 = \frac{48}{3}$

$r^4 = 16$

Taking the fourth root of both sides:

$r = \sqrt[4]{16}$

$r = 2$

3. Final Answer

The common ratio is

2. So the answer is A.